On construction of a global numerical solution for a semilinear singularly–perturbed reaction diffusion boundary value problem

by   Samir Karasuljić, et al.

A class of different schemes for the numerical solving of semilinear singularly–perturbed reaction–diffusion boundary–value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of a numerical solution were shown. After that, the uniform convergence with respect to a perturbation parameter ε on a modified Shishkin mesh of order 2 has been proven. For such a discrete solution, a global solution based on a linear spline was constructed, also the error of this solution is in expected boundaries. Numerical experiments at the end of the paper, confirm the theoretical results. The global solutions based on a natural cubic spline, and the experiments with Liseikin, Shishkin and modified Bakhvalov meshes are included in the numerical experiments as well.



There are no comments yet.


page 1

page 2

page 3

page 4


Monotone Difference Schemes for Convection-Dominated Diffusion-Reaction Equations Based on Quadratic Spline

A three-point monotone difference scheme is proposed for solving a one-d...

Parameter-uniform fitted mesh higher order finite difference scheme for singularly perturbed problem with an interior turning point

In this paper, a parameter-uniform fitted mesh finite difference scheme ...

A neural network based policy iteration algorithm with global H^2-superlinear convergence for stochastic games on domains

In this work, we propose a class of numerical schemes for solving semili...

A SDFEM for system of two singularly perturbed problems of convection-diffusion type with discontinuous source term

We consider a system of two singularly perturbed Boundary Value Problems...

hp-FEM for reaction-diffusion equations II. Robust exponential convergence for multiple length scales in corner domains

In bounded, polygonal domains Ω⊂R^2 with Lipschitz boundary ∂Ω consistin...

Continuation of global solution curves using global parameters

This paper provides both the theoretical results and numerical calculati...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.